Finite Group Databasebeta

← #29717694

Subgroups — #29717694

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839989C211yesmaximal, characteristic, complemented
2C2×#16839913C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21449270C211yesmaximal, characteristic, complemented
6#21447050C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446907C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×D42×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic, complemented
18C22×#11758200C2211yescharacteristic, complemented
19C23×#92418C2211yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic, complemented
22C22×C4⋊Dic61C2211yescharacteristic, complemented
23#16839989—24no—
24#16839913—24no—
25#16839913—24no—
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519700C2211yescharacteristic, complemented
28C2×#14519698—24no—
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic, complemented
36C2×#14519698C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic, complemented
38C2×C22⋊#92418C2211yescharacteristic, complemented
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41#16839695—21no—
42#16839685—21no—
43#16839668C2211yescharacteristic, complemented
44#16839660C2211yescharacteristic, complemented
45#16839642—21no—
46#16839622C2211yescharacteristic, complemented
47#16839620—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C23×D4×C61—21no—
53C23×D4×C61C2211yescharacteristic
54C23×D4×C61C2211yescharacteristic
55D42×C61—24no—
56D42×C61—24no—
57C2×#127×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×#120×C61—21no—
63C2×C4×D4×C61C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C23×Dic61—21no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—41no—
74C2×#11758200—41no—
75C2×#11758200—41no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519756—22no—
84#14519756—22no—
85#14519756—22no—
86#14519756—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99#14519708—22no—
100#14519700—22no—
101#14519698—22no—
102#14519698—22no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—41no—
109#14519698D414yescomplemented
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C25×C61—21no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—28no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61—22no—
125C22×D4×C61—22no—
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—21no—
129C22×D4×C61—22no—
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—41no—
134C22×D4×C61—41no—
135C22×D4×C61—41no—
136C22×D4×C61—41no—
137C22×D4×C61—44no—
138C22×D4×C61—44no—
139C22×D4×C61D411yescharacteristic
140C22×D4×C61D414yes—
141C22×D4×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147#127×C61—22no—
148#127×C61—22no—
149#121×C61—28no—
150#121×C61—22no—
151#121×C61—22no—
152#121×C61—22no—
153#121×C61D414yes—
154#120×C61—28no—
155#120×C61—28no—
156C4×D4×C61—22no—
157C4×D4×C61—22no—
158C4×D4×C61—22no—
159C4×D4×C61—22no—
160C2×C4⋊C4×C61D411yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61—21no—
165C2×C22⋊C4×C61D411yescharacteristic
166C2×C22⋊C4×C61D411yescharacteristic
167C2×C42×C61C2311yescharacteristic
168C24×C61—21no—
169C24×C61—24no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—24no—
173C24×C61—42no—
174C24×C61—42no—
175C24×C61—42no—
176C24×C61—42no—
177C24×C61—42no—
178C24×C61—42no—
179C24×C61—42no—
180C24×C61—42no—
181C24×C61—81no—
182C24×C61—81no—
183C24×C61—81no—
184C24×C61—81no—
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—28no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—44no—
218C2×D4×C61—44no—
219C2×D4×C61—432no—
220C2×D4×C61—44no—
221C2×D4×C61—42no—
222C2×D4×C61—42no—
223C2×D4×C61—42no—
224C2×D4×C61—42no—
225C2×D4×C61—44no—
226C2×D4×C61—42no—
227C2×D4×C61—81no—
228C2×D4×C61—81no—
229C2×D4×C61SD1614yescomplemented
230C2×D4×C61C2×D412yes—
231C2×D4×C61C2×D412yes—
232C2×D4×C61C2×D412yes—
233C2×D4×C61C2×D412yes—
234C2×D4×C61#4112yes—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—24no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—42no—
248C22×C4×C61—42no—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2411yescharacteristic
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—42no—
261C22×Dic61—42no—
262C22×Dic61—81no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C2×D412yes—
272C22⋊C4×C61—24no—
273C22⋊C4×C61—24no—
274C22⋊C4×C61—22no—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—22no—
277C42×C61—21no—
278C42×C61—21no—
279C22⋊Dic61—42no—
280C22⋊Dic61—42no—
281C22⋊Dic61—81no—
282#11758200—44no—
283#11758200—44no—
284#11758200—44no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—42no—
291C4⋊Dic61C2×D412yescomplemented
292#11758196—42no—
293#11758196—42no—
294#11758196—81no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418—21no—
303C2×#92418—21no—
304C2×#92418—21no—
305C2×#92418—21no—
306C2×#92418—44no—
307C2×#92418C2×D412yescomplemented
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—22no—
316C23×C61—21no—
317C23×C61—22no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—48no—
324C23×C61—48no—
325C23×C61—48no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—48no—
343C23×C61—84no—
344C23×C61—84no—
345C23×C61—84no—
346C23×C61—84no—
347C23×C61—84no—
348C23×C61—84no—
349C23×C61—84no—
350C23×C61—84no—
351C23×C61—84no—
352C23×C61—84no—
353C23×C61#12012yes—
354C23×C61C2×SD1612yes—
355C23×C61C2×SD1612yes—
356C23×C61AGL(1,ℤ/8)12yes—
357C23×C61C22×D411yescharacteristic
358D4×C61—28no—
359D4×C61—22no—
360D4×C61—22no—
361D4×C61—22no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—22no—
365D4×C61—22no—
366D4×C61—48no—
367D4×C61—48no—
368D4×C61—48no—
369D4×C61—48no—
370D4×C61—48no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—41no—
374D4×C61—41no—
375D4×C61—84no—
376D4×C61#12114yes—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—22no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—48no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61#12012yes—
400C2×C4×C61C2×SD1612yes—
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C2×#4111yescharacteristic
405C2×C4×C61H(5,𝔽2)11yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C2×Dic61—22no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—84no—
420Dic122—41no—
421Dic122—41no—
422Dic122—41no—
423Dic122—41no—
424#92418—22no—
425#92418—41no—
426#92418—41no—
427#92418—41no—
428#24432—611nomaximal, Sylow
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—22no—
434C22×C61—22no—
435C22×C61—24no—
436C22×C61—22no—
437C22×C61—22no—
438C22×C61—22no—
439C22×C61—41no—
440C22×C61—42no—
441C22×C61—41no—
442C22×C61—42no—
443C22×C61—41no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—41no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61—42no—
455C22×C61—816no—
456C22×C61—816no—
457C22×C61—81no—
458C22×C61—81no—
459C22×C61—81no—
460C22×C61—81no—
461C22×C61—81no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61#45014yescomplemented
466C22×C61C2×#12011yescharacteristic
467C22×C61D4211yescharacteristic
468C22×C61#54611yescharacteristic
469C22×C61C22×SD1611yescharacteristic
470C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C61#57611yescharacteristic
472C22×C61#57711yescharacteristic
473C4×C61—22no—
474C4×C61—22no—
475C4×C61—41no—
476C4×C61—42no—
477C4×C61—41no—
478C4×C61C2×#12111yescharacteristic
479C4×C61#53411yescharacteristic
480C4×C61D4211yescharacteristic
481C4×C61#54611yescharacteristic
482Dic61—42no—
483Dic61—81no—
484Dic61—81no—
485Dic61—81no—
486C2×D42D6111yescharacteristic
487C2×#465—611no—
488C2×#450—611no—
489C2×#450—611no—
490C22×#102—611no—
491#2417—611no—
492#2041—611no—
493#2034—611no—
494#2014—611no—
495#2000—611no—
496#1877—611no—
497#1874—611no—
498#1869—611no—
499#1864—611no—
500#1786—611no—
501C2×C61—24no—
502C2×C61—42no—
503C2×C61—44no—
504C2×C61—82no—
505C2×C61—82no—
506C2×C61#241011yescharacteristic
507C2×C61C2×#45011yescharacteristic
508C2×C61#301211yescharacteristic
509C2×C61#326411yescharacteristic
510C2×C61D4×SD1611yescharacteristic
511C2×C61#329511yescharacteristic
512C2×C61#331011yescharacteristic
513C23×D4—21no—
514C23×D4C2×D6111yescharacteristic
515C23×D4C2×D6111yescharacteristic
516C22×SD16—611no—
517C22×SD16—611no—
518C22×SD16—611no—
519C23×C8—611no—
520D42—24no—
521D42—24no—
522C2×#127C2×D6111yescharacteristic
523C2×C22⋊Q8—611no—
524C2×C22⋊Q8—611no—
525C2×#121—21no—
526C2×#121C2×D6111yescharacteristic
527C2×#121C2×D6111yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C2×D6111yescharacteristic
531C2×C4×D4C2×D6111yescharacteristic
532C22×C4⋊C4—611no—
533#465—1224no—
534#450—1224no—
535#450—1224no—
536C2×#106—611no—
537C2×#103—611no—
538C2×#102—611no—
539C2×#102—611no—
540C2×#102—611no—
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×#102—611no—
546C2×#102—611no—
547C2×#102—1224no—
548C2×C22⋊C8—611no—
549C2×C22⋊C8—611no—
550C2×C22⋊C8—611no—
551#398—1221no—
552#396—1221no—
553#391—611no—
554#389—611no—
555#386—1221no—
556#380—611no—
557#380—1221no—
558#340—611no—
559#340—611no—
560#336—611no—
561#336—611no—
562C61#2443211yescharacteristic, complemented, Sylow
563C25—21no—
564C25—21no—
565C22×Q8—611no—
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4C22⋊D6111yescharacteristic
587C22×D4C22⋊D6114yes—
588C22×D4C22×D6111yescharacteristic
589C22×D4C22×D6111yescharacteristic
590C22×D4C22×D6111yescharacteristic
591C23×C4—21no—
592C23×C4—1221no—
593C23×C4C22×D6111yescharacteristic
594C23×C4C22×D6111yescharacteristic
595C2×SD16—1222no—
596C2×SD16—1222no—
597C2×SD16—1222no—
598C2×SD16—1222no—
599C2×SD16—1222no—
600C2×SD16—1222no—
601C2×SD16—2441no—
602C2×SD16—2441no—
603C2×SD16—2441no—
604C22×C8—611no—
605C22×C8—611no—
606C22×C8—611no—
607C22×C8—611no—
608C22×C8—1222no—
609C22×C8—1222no—
610C22×C8—2441no—
611#127—22no—
612#127—22no—
613C22⋊Q8—1222no—
614C22⋊Q8—1222no—
615C22⋊Q8—1222no—
616C22⋊Q8—2441no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121C22⋊D6114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—1222no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—2441no—
637C2×C4⋊C4C22⋊D6111yescharacteristic
638C2×C4⋊C4C22×D6111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4C22⋊D6111yescharacteristic
646C2×C22⋊C4C22⋊D6111yescharacteristic
647C2×C42C22×D6111yescharacteristic
648#106—1222no—
649#103—1222no—
650#102—614no—
651#102—1222no—
652#102—1222no—
653#102—1222no—
654#102—1222no—
655#102—1222no—
656#102—1222no—
657#102—1222no—
658#102—2441no—
659C22⋊C8—1222no—
660C22⋊C8—1222no—
661C22⋊C8—2441no—
662#95—1221no—
663#95—1221no—
664#95—1221no—
665#95—1221no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×C22⋊D6111yescharacteristic
684C24C2×C22⋊D6111yescharacteristic
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—24no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4#1175820014yescomplemented
734C2×D4D4×D6112yes—
735C2×D4#1175822412yes—
736C2×D4C2×C22⋊D6112yes—
737C2×D4C2×C22⋊D6112yes—
738C2×D4C2×C22⋊D6112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—4881no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4C2×C22⋊D6111yescharacteristic
761C22×C4C2×C22⋊D6111yescharacteristic
762C22×C4C2×C22⋊D6112yes—
763C22×C4C2×C22⋊D6112yes—
764C22×C4C2×C22⋊D6111yescharacteristic
765C22×C4C2×C22⋊D6111yescharacteristic
766C22×C4C23×D6111yescharacteristic
767SD16—2444no—
768SD16—2444no—
769SD16—2444no—
770C2×C8—612no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—2444no—
783C4⋊C4—21no—
784C4⋊C4—22no—
785C4⋊C4—612no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—4881no—
792C4⋊C4—2442no—
793C4⋊C4—2442no—
794C4⋊C4—2442no—
795C4⋊C4C2×C22⋊D6112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—4881no—
802C22⋊C4—2442no—
803C22⋊C4—2442no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—21no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#1451974612yes—
852C23C2×#1175820012yes—
853C23C2×#1175820012yes—
854C23#1451980312yes—
855C23C22×C22⋊D6111yescharacteristic
856Q8—2441no—
857Q8—2441no—
858Q8—2441no—
859Q8—2441no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#1451974914yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—48no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—1222no—
902C2×C4—4884no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4#1451974612yes—
915C2×C4C2×#1175820012yes—
916C2×C4C2×D4×D6111yescharacteristic
917C2×C4C22×C22⋊D6111yescharacteristic
918C2×C4C22×C22⋊D6111yescharacteristic
919C2×C4C2×#1175822411yescharacteristic
920C2×C4#1451982211yescharacteristic
921C2×C4#1451982211yescharacteristic
922C8—1222no—
923C8—2441no—
924C8—2441no—
925C8—2441no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—24no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—41no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#1683991314yescomplemented
963C22C2×#1451974611yescharacteristic
964C22D4×C22⋊D6111yescharacteristic
965C22#1684040611yescharacteristic
966C22C22×#1175820011yescharacteristic
967C22C2×#1451980311yescharacteristic
968C22#1684056511yescharacteristic
969C22#1684057311yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—41no—
975C4—4881no—
976C4—4881no—
977C4—4881no—
978C4—2442no—
979C4C2×#1451974911yescharacteristic
980C4#1684032111yescharacteristic
981C4D4×C22⋊D6111yescharacteristic
982C4#1684040611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2#2144919311yescharacteristic
989C2C2×#1683991311yescharacteristic
990C2#2145512311yescharacteristic
991C2#2145729511yescharacteristic
992C2D4×#1175820011yescharacteristic
993C2#2145764311yescharacteristic
994C2#2145784011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×D42×C61C2
socleC23×C61C22×D4
hypercenterC2×D42D61
hypocenterC61#24432
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16839989C2semidirect
2. C2×#16839913C2semidirect
3. C2×#16839913C2semidirect
4. C22×#14519698C2semidirect
5. #21449270C2semidirect
6. #21447050C2semidirect
7. #21447005C2semidirect
8. #21446907C2semidirect
9. #21446822C2semidirect
10. #21446153C2semidirect
11. #21446137C2semidirect
12. #21446112C2semidirect
13. #21446080C2semidirect
14. #21445750C2semidirect
17. C22×#11758200C22semidirect
18. C22×#11758200C22semidirect
19. C23×#92418C22semidirect
20. C2×#14519756C22semidirect
21. C2×#14519756C22semidirect
22. C22×C4⋊Dic61C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519700C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519698C22semidirect
34. C2×#14519698C22semidirect
35. C2×#14519698C22semidirect
36. C2×#14519698C22semidirect
37. C2×#14519698C22semidirect
38. C2×C22⋊#92418C22semidirect
39. C2×C22⋊#92418C22semidirect
40. C2×C22⋊#92418C22semidirect
43. #16839668C22semidirect
44. #16839660C22semidirect
46. #16839622C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
109. #14519698D4semidirect
229. C2×D4×C61SD16semidirect
291. C4⋊Dic61C2×D4semidirect
307. C2×#92418C2×D4semidirect
465. C22×C61#450semidirect
562. C61#24432semidirect
733. C2×D4#11758200semidirect
962. C22#16839913semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168399892
C2×#168399132
C22×#145196982
#214492702
#214470502
#214470052
#214469072
#214468222
#214461532
#214461372
#214461122
#214460802
#214457502
C2×D42×C612
#2443261